You don't need to apologise again. I think any sane person realizes you were a bit foolish but little more. I'm not sure why Acker is on this particular moral crusade but I'm now starting to think it's him/her which is starting to be inappropriate by dragging this on.
This. Off-piste can mean anything from skiing along the side of a marked piste to the wilderness. Going off-piste isn't irresponsible per se with a 14 year old.
It is also worth noting that every skier/snowboarder falls over. Falling over and banging your (helmeted) head on a rock strikes me...
Yes, if the injury is serious enough. I have seen people air-lifted from the slopes numerous times. It's no big deal at a ski-resort and is covered by your insurance.